Global Optimization for Solving Linear Multiplicative Programming Based on a New Linearization Method

This paper presents a new global optimization algorithm for solving a class of linear multiplicative programming (LMP) problem. First, a new linear relaxation technique is proposed. Then, to improve the convergence speed of our algorithm, two pruning techniques are presented. Finally, a branch and bound algorithm is developed for solving the LMP problem. The convergence of this algorithm is proved, and some experiments are reported to illustrate the feasibility and efficiency of this algorithm.

[1]  Kristin P. Bennett,et al.  Bilinear separation of two sets inn-space , 1993, Comput. Optim. Appl..

[2]  Peiping Shen,et al.  Linearization method for a class of multiplicative programming with exponent , 2006, Appl. Math. Comput..

[3]  Harold P. Benson,et al.  Outcome-Space Cutting-Plane Algorithm for Linear Multiplicative Programming , 2000 .

[4]  Michael C. Dorneich,et al.  GLOBAL OPTIMIZATION ALGORITHMS FOR CHIP LAYOUT AND COMPACTION , 1995 .

[5]  I. Androulakis,et al.  Solving long-term financial planning problems via global optimization , 1997 .

[6]  Yuelin Gao,et al.  Outcome-Space Branch and Bound Algorithm for Solving Linear Multiplicative Programming , 2005, CIS.

[7]  Sanyang Liu,et al.  Global minimization of a generalized linear multiplicative programming , 2012 .

[8]  Siegfried Schaible,et al.  Finite algorithm for generalized linear multiplicative programming , 1995 .

[9]  Bing-Yuan Cao,et al.  A Simplicial Branch and Bound Duality-Bounds Algorithm to Linear Multiplicative Programming , 2013, J. Appl. Math..

[10]  Nikolaos V. Sahinidis,et al.  Global Optimization of Multiplicative Programs , 2003, J. Glob. Optim..

[11]  Guorong Wu,et al.  A new global optimization approach for convex multiplicative programming , 2010, Appl. Math. Comput..

[12]  Hiroshi Konno,et al.  Global minimization of a generalized convex multiplicative function , 1994, J. Glob. Optim..

[13]  Xue-gang Zhou.  Global Optimization of Linear Multiplicative Programming Using Univariate Search , 2014 .

[14]  Bing-yuan Cao,et al.  Global optimization method for linear multiplicative programming , 2015 .

[15]  Nguyen V. Thoai.  A global optimization approach for solving the convex multiplicative programming problem , 1991, J. Glob. Optim..

[16]  Robert J. Vanderbei,et al.  Robust Optimization of Large-Scale Systems , 1995, Oper. Res..

[17]  I. E. Grossmann,et al.  Alternative Bounding Approximations for the Global Optimization of Various Engineering Design Problems , 1996 .

[18]  Xue-Gang Zhou,et al.  A method of acceleration for a class of multiplicative programming problems with exponent , 2009 .

[19]  Takahito Kuno.  Solving a Class of Multiplicative Programs with 0–1 Knapsack Constraints , 1999 .

[20]  R. Horst,et al.  Global Optimization: Deterministic Approaches , 1992 .

[21]  Susan W. Palocsay,et al.  Image space analysis of generalized fractional programs , 1994, J. Glob. Optim..

[22]  Jianping Wang,et al.  An optimization algorithm for solving a class of multiplicative problems , 2014 .